 Okay, well welcome back from lunch So I just want to recap briefly where we've been before we start forging ahead so remember that where we started this morning was essentially from the most basic set of assumptions on Observables of dark matter, so we have rotation curve measurements, which provide the most robust Indication that there is a considerable fraction of missing matter in the universe And then based off of those rotation curve measurements we've built up this picture of how galaxies are surrounded by these very large halos of dark matter and The presence of those halos then lets us Put constraints very generic constraints on the mass of the individual dark matter particles So these generic constraints remember for the bosonic case Or something like 10 to the minus 22 EV and for the fermionic case were more like 0.7 KV and Then the last thing we did was to add An additional layer to this and say okay well If we start off with the assumption that dark matter halos form then this must be true But we're going to add to that an additional assumption that the dark matter was in Thermal equilibrium in the early universe and if we add that assumption on to all of this We can then end up motivating the case that the dark matter is weak scale so on more like a hundred GV But there's a lot of caveats that come with this as I was explaining at the end of the last lecture We don't have to do much to change this picture of The thermal dark matter picture to get different mass scales But I want to focus on the weak scale picture for now mainly because it's played such an important role in designing experiments to test for dark matter and so What we're going to do now is discuss some classes of these experiments And I want to tell you kind of what the current status is in terms of testing this hypothesis and Where we're going to want to go from from here Sets of experiments that I'm going to try to get to in the next hour the first is called Direct detection and The second is called indirect detection there's a lot more than just this and in particular One category that I probably not going to have time to get to now But we can definitely discuss more in a discussion session if there's interest is LHC searches, but there's a lot more so It's only because of the limitations of time that I'm going to cover to not because these are the only possibilities that are there so direct detection experiments are ground-based and Specifically what we're doing here is looking for what happens when you have a dark matter particle and it Scatters off of an atomic nucleus direct detection is No, I'll call it sky-based in the sense that here what we're looking for is signatures of the dark matter particles Annihilating in the Milky Way Giving us things that could like, you know, W bosons or Z's or quarks Which then can end up giving us photons down the road and then we can search for very high-energy gamma rays as a way of Telling whether or not the dark matter actually annihilated in this fashion So let's start off with the direct detection case first and then and then get to the indirect detection Scenario like I said for direct detection What do you essentially want to do is you get a target of material? But crystal or something like that or in some case Xenon gas and you put it deep underground. So most of these labs are at the bottom like In mines or at the bases of mountains Mainly because you need to shield your experiment from any kind of you know, whatever backgrounds are there and You so you put this tub of material there and you wait Essentially what you're waiting for is the fact that you know, there's dark matter particle streaming around here going through us All time of day and you hope that one of those particles will ultimately end up Hitting one of the nuclei in your target and that nucleus would just jiggle a little bit and When it jiggles a little bit it might admit heat or phonons or something like that which you can actually detect So you need incredibly sense of detection mechanisms In order to be able to do this and to put your experiment also very deep underground so what are the energy scales of what we're talking about here if so the Recoil energy of the nucleus in one of these experiments So when I mean my recoil energy is just the energy of the nucleus after it's scattered with the dark matter particle that recoil energy as roughly 50 keV times dark matter mass inversely proportional to the nuclear mass and most of these experiments at least currently Start to lose their sensitivity When the nucleus just has an energy as a recoil energy less than 10 keV or so so So the current thresholds for these experiments are Roughly 10 keV. So this will give us an idea then of what the mass ranges are that these experiments can look at for So for example, if I had a xenon target So some of the most sensitive experiments right now are using xenon, which is why I've chosen that then the nuclear mass for xenon is Roughly 120 GeV and so we can see that when the dark matter mass is Around 50 or 100 gEV This kind of experiment would have optimal sensitivity because the recoil energy of the the nucleus is going to be large enough But it will lose sensitivity for dark matter masses If for dark matter masses that are less than on the order of 10 keV because in that Regime then we're talking about recoil energies that are only a few keV And that's kind of below the thresholds of what these experiments can actually detect These experiments then are really primed to look in this region of weak-skilled dark matter Which is you know, there's a reason that they've been designed this way. They're really aimed at testing the miracle and their sensitivities are getting really really good right now, so Probably in you know the in the next round of these experiments is going to really push into a region where if they see it They're going to see it, you know, if it's there, they're going to see it and if they don't see it It's going to really call into question Whether or not this was the right place to be starting from So how do we actually model these kinds of interactions? The relevant quantity here is the scattering rate of the dark matter off the nucleus, right? And we're talking about a scattering where The nucleus doesn't break apart. So the kinetic energy the incoming kinetic energy for the the dark matter is on the order of tens of keV Whereas the nuclear binding energies Are more like MEV scale So we can treat this system as just the dark matter scattering off the nucleus as a whole and not the dark matter scattering off of the individual constituents of the nucleus So that's an additional level of you know Complication that we're going to need to take into account but like I said the relevant quantity is the scattering rate and usually you want to know it as As a the differential rate as a function of the recoil energy of the nucleus after the scattering and This is going to be equal to the the number density of the dark matter times the Interaction cross-section the velocity average interaction cross-section and we usually do this in terms of the Per unit detector mass. So that's why I put a one over mass for the nuclear target here oops This should be d sigma and writing this out more fully So you can see all of the components that come into play here When I take this velocity average here, what I'm doing is Multiplying by the velocity distribution of the dark matter in the Milky Way and Then there's the d sigma The ER here One theme that will become apparent in the examples We're going to go through in the next hour is the fact that the dark matter is non-relativistic in the Milky Way In in both examples is going to end up playing a direct role in the Well in the computation of the observable and in some cases really does kind of change what we expect to see so This integral for example here is I'm integrating from the minimum value that the dark matter velocity can take to the maximum value The maximum value for the dark matter velocity in the Milky Way is roughly like I said before 550 kilometers per second Which you can just estimate for yourself is the escape velocity for a particle in a halo That's the size of the Milky Way and This minimum velocity Is determined by the scattering kinematics So it's the minimum velocity that the dark matter needs to cause the nucleus to recoil with this energy so This is the minimum velocity for a certain nuclear Recoil and to get the expression for the minimum velocity. It's literally freshman mechanics So like bowling balls like just figuring out What the the minimum scattering velocity is that that you need there? Velocity distribution that's going in here is the velocity distribution in the lab frame So we need to be a little bit careful because remember Our picture here. So here's the center of the galactic disc and let's say we're living here The experiment is running on earth. So it's running well here where the Sun is and We want to know what the velocity distribution is here not the velocity distribution relative center of the galaxy But our models for f of v Always describe the velocities relative to here to the center part of the galaxy so what we need to do is To get the velocity distribution in the lab frame We have to take the velocity the distribution in the galactic frame and just do a Galilei and transformation to it where we add The velocity of well, I should just So it's we're adding to it the velocity of the earth relative to the center of the galaxy Okay, this is just given by the velocity of the Sun relative to the center of the galaxy Plus the velocity of the earth Relative to the Sun so this is Sun relative to center and this is earth relative to Sun So just to give you a sense for what the order of magnitudes are here So the motion of the Sun relative to the center of the galaxy if I take the Magnitude of that it's roughly two hundred kilometers a second and If I take the magnitude of this Velocity of the earth relative to the Sun That's roughly 30 Kilometers per second so I can tailor expand this Yes, okay Well, I can write this like this Where what I've done is to now factor out the velocity of the Sun that leaves me with one here and then this is The magnitude of the Velocity of the earth in the direction of the Sun Over the velocity the speed of the Sun So this thing is just a small number because what we're doing is comparing 30 to 200 and this term here is meant to describe the fact that the the earth's motion around the Sun is periodic with a period of one year, right if I put this Inside here and then expand The distribution in terms of epsilon What I get in this case is that My first order term is just the velocity of the dark matter plus the velocity of the Sun and then the second order term is going to be Some small contribution That depends on The yearly rate where this is the first derivative of the of the distribution function So that's just the Taylor expansion around the small parameter epsilon. So if I substitute this Into the differential rate here What I find is that I can write the rate out as a Taylor expansion It's going to have the first term is going to be constant in time And then there's going to be higher order terms such as this one Which depends on the time of year So this term here is the unmodulated rate and this one here Gives you the rate that actually modulates annually So this annual modulation piece is coming from the fact that the earth is rotating around the Sun Kind of give you a sense for what an experiment is actually looking for I'm going to do just a very simple order of magnitude calculation for the unmodulated rate So if I take I'm only going to look at the unmodulated piece. So this unmodulated piece is Going to be proportional to the integral From the minimum velocity of the dark matter to its maximum velocity, which is just the escape velocity integral over V The velocity distribution shifted by the solar the velocity of the Sun and I get a one over V that's coming from the fact that d sigma de and recoil is Proportional to one over velocity squared Which I don't have time to show today, but you can you can show this explicitly So it gives you gives you this form here This velocity distribution is usually taken to be Maxwell-Boltzmann Distribution and So if I put that in I can actually solve for this exactly so V min to V escape V V V e to the minus V squared over V not squared. I'm only keeping the most important terms But here I'm making the assumption that f of V is just Maxwell-Boltzmann and then this minimum scattering speed here comes from Just the like I mentioned before the scattering kinematics and if you solve that out You'd find that this is just the mass of the nucleus Recoil energy over twice the reduced mass squared So if I put all of this in here and just kind of till the level figure out what this differential rate is I get e to the minus recoil energy So it's exponentially falling in recoil energy so an experiment If they actually see a signal What they would find is that For the simplest kind of models dark matter models Their signal should be falling off like this as a function of of recoil energy So this would be the signal that they'd be Aiming to to see now depending on how I change the particle physics model and also How I change how the dark matter interacts with the nucleus that can change as well So one case is just to illustrate I can have in certain models The dark matter scatter in elastically so it comes in my dark matter particle comes in It's the nucleus the nucleus scatters and Then the dark matter up scatters So if it comes in with if I label the initial state chi it might go to some new state chi prime Where the mass of the chi prime? Is some small difference? It's a little bit larger than the mass of the original dark matter particle So, you know these kinds of inelastic Scattering events can happen in more complicated models where you add an additional state. That's pretty close in mass to your dark matter if this happens then your minimum scattering velocity tends to be larger and The well And then your scattering rate would actually look more like This so these experiments actually have the ability based on the differential rate that they're observing to be able to tell the difference between different Like basic assumptions that you'd be making about the dark matter interactions with the baryons with the nucleus There's an additional component that's very important because it could potentially be the key in terms of distinguishing these kinds of signals from background And that's coming from the time dependence here, which I've ignored up until this point That time dependence says that your signal should modulate annually So you kind of want to sit there and look at this scattering happen for long periods of time because if it is dark matter then You should expect there to be this annual modulation to your signal and you could use that as a way of trying to distinguish Your signal from any potential backgrounds that could be faking it So it's an important component that comes into play. Let me tell you what the current status is for These experiments So I'm going to sketch the limits up on the board For the actual detailed version. I'm going to point you to the notes That are online. So the limits are usually shown On a plane of where the horizontal axis is the dark matter mass in GEV and the vertical axis is the cross section the interaction cross section, but in particular, it's the cross section for dark matter interacting With with a part on pull this up so I can actually Try to be yeah with the nucleon The better way of writing it. Okay, and in units of centimeter squared. So here's what we've got so most of the limits Look something like the tightest one so the tightest bound right now is coming from an experiment called lux which has a xenon target Their sweet spot. So where they have maximum sensitivity is around 50 GV and Then they lose sensitivity Around 10 GV which is consistent with the estimates that we were making earlier But that's what their actual limit plot looks like so the fact that they lose sensitivity coming down this way is because the recoil energy of the nucleus gets too small and they can't pick up the jiggle anymore and The reason they lose sensitivity this way just has to do with the fact that The number density of the dark matter gets smaller as you go to higher mass because number density is Actual density divided by the mass of the dark matter So this scaling here This loss of sensitivity scales as one over dark matter mass There is a whole host of experiments and they all kind of fall roughly in this regime There are other experiments now that are starting to put limits down here so one example is a super CDMS which has a germanium target and Their goal is to start probing this region at masses below 10 GV So, you know, they're starting to get some sensitivity there and then There so this is roughly 10 to the minus 42 and this is roughly 10 to the minus 45 There's on top of this a region that kind of goes like this and Below this yellow line you actually start becoming so sensitive that you can pick up coherent scattering of neutrinos off of your target So below this line You have neutrinos scattering and at that point in time You know The neutrinos scattering looks really similar to the dark matter, right? They're both neutral particles and so your experiments are not You know are now going to have to contend with the fact that they're going to have to separate out the neutrinos signal From the dark matter signal so this detector with xenon was about I think 300 kilograms on that order and The next generation of these experiments are going to be going down here So these are a ton scale Xenon detectors And they're going to be pushing really deep into this perimeter regime Just right right in here This is really important Because the region that's really well motivated theoretically Sits here this region here that I've hatched off is the region where we expect Dark matter to interact with the nucleus via exchange of the Higgs So for example diagrams like dark matter dark matter Higgs Quark quark Diagram like this would give me Scattering in this region here and you can actually estimate if you put in sort of typical couplings for dark matter with the Higgs and Higgs with the quarks that this falls roughly in this region around 10 to the minus 45 centimeters squared You know there's some there's wiggle room in there But you know this is kind of the sweet spot for it and this is precisely where the experiments are starting to push into right now So by the time that they get to the next generation versions that are going to be ton scale They will have covered the vast majority of this parameter space And so it'll be you know It's a particularly exciting period for these experiments because they're going to be looking for processes like this We know that the Higgs exists now and it you know if the dark matter interacts weekly This is pretty much the only thing that has left to interact weekly through so this is something to kind of keep an eye out for the next few years because It's you know, there's It's essentially going to be the direct test of this wimp wimp dark matter And these experiments have the sensitivity to really be able to to say something significant about that Are there questions on these direct detection and experiments before I say something about indirect. Yeah Yeah, so I mean I'm making some assumption about So there's some coupling here between the Higgs and the dark matter I am making some assumption there So that's what's giving me this kind of wiggle room I mean there's there's several orders of magnitude that this covers and that that's that wiggle room is coming from the fact that We don't know what this coupling is But after a certain point like I can't you know, I could make this as small as After a certain point this becomes so small that it's not dominantly going through that interaction anymore And so if we you know, you could still have wimp dark matter. That's That can be giving you cross sections below the scale but in order to get that you have to get cancellations So this diagram cancelling off with some other diagram your theory or some loop induced process becoming important And so it could still happen. It's just you're starting to get into very narrow slices of the allowed parameter space Oh here. Well, I can't make this arbitrarily large Yeah, this if this coupling is here it can get mass from the weak scale breaking But I can't I'm not allowed to make this coupling arbitrarily large Like I can't make this coupling infinity I mean, yeah, so burying it within the sort of allowed regions in which I can bury it puts me around here But I if I if I drive it higher than it the theory is not self-consistent anymore. So it's not yeah So in the last few minutes, let me just briefly introduce this other class of experiments So these experiments are called indirect detection mainly it's indirect because you're not You're you're aiming to observe the The after effect of a dark matter interaction For example, I can have the simplest manifestation as dark matter dark matter goes to a pair of photons If I have something like this and you know, I then let's say it's occurring. You're the center of the Milky Way I can put a satellite up in the sky that's looking for these really high-energy gamma rays that come out of this kind of interaction and What that satellite will be looking for is the counts of photons Versus their energy The background is something like this and If there was a signal there for the case where the dark matter goes directly into two photons My signal would look like a Spike so It looks something like this where the energy of the photons is Matches on to the mass of the dark matter So I would be looking for a line in the spectrum for Annihilations of this form if I had the dark matter going to let's say W's or zebozons or quarks Then what happens down the road is that these guys are going to hydronize so they're going to end up forming Mainly all like Quarks you'll get quarks in the decays of the W's or the Z's and then this will ultimately just end up forming a bunch of pions and Maisons and then the pions Give me photons So I end up getting photons from this, but it's just it sort of happens further down the road and so when I plot The the counts as a function of the photon energy in this case It looks like a broad continuum so the signal would be looking something more like this and So the essentially the energies get smeared out because they're coming from decays much further down in this chain Then in this case where they're coming directly from the annihilation and so I get a delta function spike So what are the best places to be looking for? These kinds of annihilations to maximize our chances of seeing them We want to look in locations of the sky that are going to have a lot of dark matter so that are going to be really dense and The best places are going to be the center of the Milky Way the dwarf galaxies which are Galaxies that orbit the Milky Way They're much smaller than the Milky Way and they contain very few stars. So they're dark matter dominated systems They're very clean as a result and the third Option is from annihilation coming from dark matter in extra galactic galaxies For example, we could look at the small and large Magellanic clouds We could also just sum up the contributions from all of the galaxies that we can see in the sky Limits have been put on dark matter annihilation from all of these I will show you these The situation in the center of the galaxy is confusing because there's a potential signal there And there's a lot of debate as to whether or not it's coming from astrophysics or from dark matter Happy to chat more about that during the discussion session if there's interest But for now, let me tell you about the limits coming from the dwarfs Limits are usually drawn in a plane. That's some Annihilation cross-section It's a function of dark matter mass and the relevant quantity Just to kind of guide your eye is the cross-section 10 to the minus 26 centimeters cube per second, which is the cross-section. That's relevant for thermal dark matter the current limit assuming Dark matter goes to a pair of bequarks Looks like this Where are the expected value? so so this bound here is meant to indicate the expectation for where the limit should be and This line here is what's Observed so these are limits that are coming from dwarf galaxies and The really crucial point here is the fact that the limits Even you just sort of see explicitly here by I are Starting to push down below thermal cross-sections Roughly in a mass regime that's consistent with weekly interacting massive particles. So around here So as these limits continue to tighten here We're really start, you know, we're really probing the case of 100 gv Thermal dark matter depend a lot on The quality and number of dwarf galaxies that we've actually observed When this was first published this result, I should mention these are all coming from a Fermi large area telescope When these results were published, we knew of about 25 dwarf galaxies last year saw an amazing increase in in The number of dwarf galaxies that we now know of so the dark energy survey Published several data releases and the number of dwarf galaxies we now know of is up to about 50 So we've gone from 25 up to 50 So the more of these dwarf galaxies there are the more targets We have to look at so we can point the satellite in the regions of the sky where we know the dwarf galaxies there and Just look for any excess annihilation. So it gives us more targets to look for For dark matter annihilation. So this jump in the number of dwarfs is going to be Really important for for dark matter searches and it's anticipated that you know in the coming years This number might go up to you know, several hundred potentially I mean that's based on extrapolations of how many dwarf galaxies there might actually be but as these as these Numbers increase it's going to have a direct impact on On the dark matter searches because it'll give us more places that we can look in the sky for these annihilation mechanisms, okay, so Let's see So that's kind of a very broad overview of these two classes of searches If I write down more complicated dark matter models, I can get much more interesting signatures So there's some classes of models where I can have for example the dark matter interact with itself And so for example, I can have cases where I have two dark matter particles coming in and then they exchange Massive bosons So just lots of massive bosons So essentially they feel some long-range interaction and that this happens before they actually annihilate into standard model final states and The presence of this long-range interaction can cause things like bound states of dark matter to form Which can change the spectrum of photons that we expect to see and there's some signals that We can't see if it wasn't for the fact that they were enhanced in this way So if I complicate the model a little bit, I can end up getting some really fascinating signatures that come out as a result That that really you know in cases like this I need to rethink what these limits what these limits mean for these kinds of dark matter models Okay, so I'm happy to discuss this in more detail in the discussion session Like I said, this is really only the tip of the iceberg for the types of searches that are being done for dark matter Both of these cases direct and indirect are really targeting WIMP scale dark matter But like we've discussed, you know, there's really a very wide range of possibilities And so part of the challenge and also the excitement moving forward is to think about how We'd actually want to design experiments to probe many of these other kinds of dark matter models And you know to see what we end up getting out of it because it's likely that whatever is out there is just going to End up surprising us and we're going to want to be ready For whatever that may end up being So I'm happy to take any more questions now. Otherwise we can continue discussing again after after the break. Thank you